Applying Genetic Algorithms to Convoy
Scheduling
Edward M. Robinson1 and Ernst L. Leiss2
1 Binary Consulting, Inc. 4405 East-West Highway, Suit 109,
Bethesda, MD 20814 USA, [email protected]
2 Ernst L. Leiss, Dept. of Computer Science, University of Houston,
[email protected]
Abstract. We present the results of our work on applying genetic algorithms
combined with a discrete event simulation to the problem of convoy
scheduling. We show that this approach can automatically remove conflicts
from a convoy schedule with the ability for the human operator to search for
better solutions after the initial conflict free schedule is obtained. We
demonstrate that it is feasible to find a conflict free schedule in a few minutes
on a common workstation or laptop. The system is currently being integrated
into a larger Transportation Information System that regulates highway
movement for the military.
1
Introduction
The objective of this work is to automatically remove conflicts from a convoy
schedule. The technique applied was to use a genetic algorithm approach combined
with a simulation engine and real world data.
1.1 Convoys
Convoys are used to move equipment and people from one point to another [1],
with equipment being trucks and vehicles that can perform the movement. A large
military container ship can carry 800 containers and 1200 vehicles, which must be
unloaded and moved quickly from the port to their final destination. This movement
is managed by a Movement Control Team (MCT) that must organize and schedule
the convoys and, at the same time, must integrate the convoy movement with the
ongoing transportation of services within their area of responsibility. Data obtained
from experienced transporters (human operators) report that 100 convoys per day are
not uncommon. The challenge facing the MCT is to schedule the convoys and daily
movements so that roads are uniformly used and, more importantly, that two or more
2
Edward M. Robinson1 and Ernst L. Leiss2
convoys do not run into conflict for a given resource. The term used by transporters
for removing conflicts from a schedule is “deconfliction”.
An example of a conflict occurs when two convoys attempt to exit the same gate
(assuming that only a single convoy at a time will use the gate) at the same time.
Other conflicts include two convoys trying to cross (at right angles) through a single
intersection, one convoy passing another on a single route leg, and two convoys
merging onto the same highway segment. While these conflicts are most common,
other issues can arise based on local rules and regulations so the system must be able
to be extended to support these cases. Our system currently detects convoys
attempting to merge or cross at a single node and one convoy overtaking another.
Military doctrine restricts convoys to one at a time on a given road segment in most
cases and further requires a 20-30 minute gap between convoys. This aspect is being
added to the automatic conflict removal module as it is being integrated into the
target system.
The workflow for convoy scheduling starts when a convoy commander submits
a request for a convoy clearance to the MCT. This request includes a list of trucks
and other vehicles, a route or strip map, the origin and destination, and a requested
time of departure. The MCT will either grant the request without changes or change
the departure time or route if the situation requires it.
1.2 Convoy Scheduling
To determine if convoys will run into conflicts, information is supplied regarding
the speed of the convoys, the maximum speed on each road segment, the number of
vehicles and their dimensions, the required gaps between vehicles, and the routes in a
common format. The length of the convoy and speed along a given segment (the
lesser of the convoy speed and segment speed) can be used along with the convoy
length to calculate the pass time of the convoy (the time elapsed between lead
vehicle and trail vehicle crossing the same point. Figure 1 illustrates convoy structure
and length.
Fig. 1. Example of convoy organization.
Using the speed of the convoy and the pass time each convoy can be stepped
forward in time along its given route tracking the times that the lead and the trail
pass a given node. A conflict occurs when the lead from another vehicle reaches a
node between the crossings of the lead and trail of the original convoy. Another
conflict will occur if one convoy passes another on a single segment. This can be
observed if the convoys reach the node at the end of the segment in a different order
Applying Genetic Algorithms to Convoy Scheduling
3
than they passed the node at the beginning of a segment. We coin the term
“inversion” for this kind of conflict.
1.3 Goals
Our primary goal for this project was to create a module for a Transportation
Information System (TIS) that automatically adjusts an initial schedule to remove
conflicts. Allowable changes included adjusting the departure time or selecting an
alternate route (with the same origin and destination). The suitability of new
schedules is ranked according to removal of all conflicts followed by a weighted
evaluation of the changes to the schedule including closeness to requested departure
time, convoy priority, and number of route changes.
Additional goals include support for incremental rescheduling based on changes
in the field and extensibility to take into account local rules, guidelines, and
opportunities (such as using roadside rest areas to allow one convoy to pass another).
A final constraint for all modules in the TIS is that the system must be field portable,
i.e., it must be able to operate on a laptop without Internet access. Implied by this is a
relative speedy operation; execution times of several hours are not conducive to
responsiveness to developments and changes in the field. Execution times within 10
minutes are considered acceptable as conveyed by experienced transportation
personnel.
2
Related Work
Convoy deconfliction is unique enough that there is limited amount of research
on the subject. However, there do exist systems that automatically remove conflict
from schedules as well as papers describing work on building conflict free convoy
schedules while minimizing total time.
2.1 MOBCON
MOBCON [1,2] is a mature system used for scheduling convoys within the
continental United States (CONUS). There are no publications that discuss the
algorithm used to remove conflicts from convoy schedules. It was only assume that
MOBCON performed this function. However, MOBCON is tightly integrated with
the rules and regulations for executing convoys and obtaining permission from each
state to allow the convoy to use its highways, which would make it difficult to
extract an extensible core algorithm. Also, MOBCON is a mainframe application,
which would violate the requirement to be field portable.
2.2 Convoy Movement Problem (CMP)
4
Edward M. Robinson1 and Ernst L. Leiss2
The Convoy Movement Problem (CMP) attempts to find the minimum overall
time for routing multiple convoys from the origins to destinations. [3] showed that
the problem is NP-complete in simple cases, and more complicated in more realistic
situation. The problem is the aimed-for optimality of a solution. Optimality is not
required – at present, convoys are scheduled manually, with very limited
computational support; therefore, the presently applied scheduling algorithms are
obviously not optimal. Consequently, it is far more useful to apply heuristics in some
form, which will improve solutions, but do not necessarily guarantee optimality. The
approach taken in [4] recognized this and combined genetic algorithms with a branch
and bound approach; however, the results, especially the time requirements of their
programs rendered it rather impractical.
3
Our Approach
Our approach to meeting the objectives described in section 1.3 combines genetic
algorithms with a simulation engine. The decision to use genetic algorithms (GA)
was based on discussions with domain experts in convoys and interaction in the past
with researchers in the GA area that emphasized the speed of recalculation in the
face of changing conditions.
There exist many conflict free schedules for a given set of convoys (a trivial
approach would be to start each convoy on a different day). An optimal schedule was
believed to be too expensive to calculate (since at best it is NP-complete) but
discussions with domain experts determined that an optimal schedule was not the
goal. The goal was to find a conflict free schedule that favored the priorities and
original request times. Such a goal is ideal for a heuristic approach.
Further discussion with domain experts showed that the conditions for conflict
and techniques for working around conflict change from location to location. The
ideal system would support easy extension and the ability to adapt local business
rules into the solver. Experience recommended the use of a discrete event simulation
as the method for evaluating a schedule for conflicts. The simulation approach would
have the added benefit of being easy to explain and validate with the domain experts
as changes were made.
3.1 Genetic Algorithm Structure
The DNA string in our genetic algorithm consists of offset times to be applied to
the requested departure time to determine the actual departure time for the convoy.
This offset is taken from a set of offsets, which is a configuration parameter. A nice
benefit of this approach is that the resulting DNA string when combined with the
convoy names is straightforward to read (ex: convoy 1 starts 15 minutes earlier,
convoy 2 starts on time, convoy 3 starts 20 minutes later). In practice, the offsets are
generally in multiples of 5, 10, or 15 minutes.
Mutation was applied by randomly selecting a given offset entry and selecting a
randomly different offset time. Selecting a crossover point at random between two
randomly selected “parents” from the top half of the population and creating two
Applying Genetic Algorithms to Convoy Scheduling
5
new children by crossing the parent DNA strings at the crossover point. Each single
string represented an alternate schedule and individual offsets (convoys) were treated
independently.
Randomly selected offsets were used to create the initial population strings along
with a single zeroed out string to represent the schedule “as-is” to ease tracking
performance. The following steps were applied to each generation:
• Mutate
• Breed
• Evaluate
• Sort
The evaluation step was used to determine the fitness of each string (schedule),
which combined a simple evaluation of weights with the simulation of the schedule
to determine the number and type of conflicts.
The fitness function was determined through interviews with experienced
transportation personnel to closely support transportation mission objectives.
Inversions were considered worse than contention for a given node and the presence
of any conflict was considered worse than other considerations such as closeness of
actual departure time to requested departure time, closeness of predicted arrival time
to requested arrival time, and favoring a higher priority to selected convoys that
might carry fuel or ammunition. Several techniques were tested and the final
technique to calculate the fitness uses
100
10
" inversions + conflicts +
1
" offsets
3.2 Simulation
!
A discrete event simulation (see Fig. 2) was used to step each convoy through its
route starting at the time determined by adding the offset to its requested departure
time. Active agents were used to model the lead and trail vehicles; route nodes and
legs (edges) were modeled as resources, which were used to track which convoy was
utilizing the node at a given time. A global simulation clock was used to determine
which event occurs next and to issue an event trigger to the agent that had scheduled
the event. Node resources allow locking by the head of a convoy and unlocking by
the trail of a convoy. If the node is already locked (indicating that this resource is
already being used by another convoy), the node resource will flag the conflict with a
monitor that keeps count of all conflicts encountered.
6
Edward M. Robinson1 and Ernst L. Leiss2
Fig. 2. Object model used to execute the simulation.
Simple queues located with leg resources are used to detect inversions. A
convoy is added to the queue when it enters a leg of a route ; it is removed from the
queue when it exits it. A convoy that overtakes the first convoy would attempt to
remove itself out of order and the leg resource would register that with a monitor that
keeps a count of inversions.
3.3 Convoy Data
Convoy data were taken from the database used to test the TIS as well as
generated from templates. Also, data collected from a simulation of a single convoy
were vetted against documented training examples. These data were stored in an
object model serving the simulation. The object model is illustrated in Figure 3.
The convoy schedule holds all of the convoys and their information. Routes are
shared amongst the convoys since that is the case in the field. Additionally, military
doctrine allows for convoys to be hierarchically structured into march-units, serials,
and columns. This is modeled with a tree structure in the object model to simplify
logic. Vehicle information is used to provide the length of the vehicle, which is used
in turn to calculate convoy length and pass time. Additionally, the height and weight
of a vehicle is needed to determine the validity of switching routes. If an alternate
route has a low or weak bridge the convoy may not be able to traverse that route.
Also, cargo contents may impact the ability of a convoy to cross a given leg. For
example, fuel trucks are not allowed to pass near water in some European countries.
Applying Genetic Algorithms to Convoy Scheduling
7
Fig. 3. Object model used for representing convoy in simulation.
4
Results
We tested our system using convoy sizes of 10, 25, and 50 each with 30 vehicles.
We were able to minimize to reach conflict free schedule within 50 generations for
each test case by varying the size of the time window. The results of these runs are
given in Table 1. Each convoy requests departure between 9AM and 8PM on a single
day. In each case, a conflict free schedule is found within a minute on a reasonably
powerful workstation (a 2.7 GHz dual processor PowerPC). The code is written in
Java 1.4.2 with no performance tuning or the use of the HotSpot server runtime.
Tests were run on Pentium 4 laptops used in the field with comparable performance
(within 2 minutes maximum processing time).
Table 1. Window sizes were adjusted to find a conflict free solution in fewer than 50 steps.
Number of
convoys – Size
10 – 30
25 – 30
50 – 30
Steps to first
conflict free
23
40
36
Time window
in minutes
150
480
2160
Average offset
in minutes
79
288
1131
Elapsed time in
seconds
8.3
33.8
57.7
8
Edward M. Robinson1 and Ernst L. Leiss2
The time window selected has a significant impact in the performance of the
search algorithm. We constructed a test to compare the impact of window size on
performance on the 25-convoy test data. The results in Table 2 show this
performance. Each test run took approximately 2 minutes of user time to complete
150 steps.
Table 2. Test case showing the effect of changing window size on 25convoys.
Time window Steps to first
in minutes
conflict free
360
62
390
36
420
31
450
44
480
46
Average offset
at step 50
141.3
170.2
178.2
233.1
173.0
Average offset
at step 100
109.6
121.7
135.6
154.6
150.0
Average offset at
step 150
110.0
92.9
98.0
117.1
125.7
Clearly the system is sensitive to the time window size with an apparent
minimum average offset. This demonstrates the utility of having a human operator in
the loop. The operator can guide the solution according to the tactical situation. If
speed is the preeminent condition, the operator will stop the simulation as soon as a
conflict free schedule is achieved. However, if more time is available, the operator
can adjust the time window as well as allow the simulation to run longer in order to
achieve a better solution.
5
Conclusion and Future Work
We have shown that a field portable system can be implemented to automatically
find a conflict free schedule given an initial convoy schedule. The system is able to
find a solution within a minute for up to 50 convoys and can continue searching
according to the needs of the human operator. This system is currently being
integrated into an existing TIS in order to be fielded in the 2006 to 2007 timeframe.
In the future, we will be improving the performance of the code through standard
tuning techniques and developing a larger set of test scenarios to analyze common
situations (such as unloading large container ships or return trip deployment). We
will also investigate different techniques manage the sensitivity of the time window
on find better solutions. Finally, the transportation community is interested in
utilizing the same techniques for non-convoy transportation uses such as supply
chain management and backhaul optimization.
6
References
1. Army Field Manuals: FM 55-1, FM 55-30, and FM 55-65. GlobalSecurity.org
http://www.globalsecurity.org/military/library/policy/army/fm/index.html
Applying Genetic Algorithms to Convoy Scheduling
9
2. R.J. Shun, Army Logistics Management College (ALMC). Automating Convoy
Operations. http://www.almc.army.mil/alog/issues/NovDec97/MS214.htm
3. P. Chardaire, G.P. McKeown, S.A. Verity-Harrison, and S.B. Richardson, "Solving a
Time-Space Formulation for the Convoy Movement Problem", Operations Research, vol.
53, no. 2, pp. 219-230, 2004.
4. Y.N. Lee, G.P. McKeown, and V.J. Rayward-Smith, The Convoy Movement Problem with
Initial Delays, Modern Heuristic Search Methods (John Wiley & Sons, 1996).